The magnetic compass operates by aligning itself with the earth's magnetic field to indicate the direction to magnetic north. More specifically, it aligns itself with lines of magnetic flux, which converge at the magnetic north and south poles. This alignment results in numerous compass errors, which the pilot must be aware of to properly use compass indications.
Variation
The difference between magnetic north and true north is the magnetic variation, and varies based on where you are located. In one place the variation might be zero degrees, meaning that the compass indication is the same as true north. In another place, the compass might indicate 20 degrees different from true north. To allow pilots to compensate for variation, it is marked on aeronautical charts and noted on the A/FD.
Deviation
The compass is also sensitive to magnetic fields generated by electrical equipment on the aircraft. This results in compass deviation. Deviation is marked on the compass correction card and is normally less than a few degrees.
Lead and Lag Errors
The earth's magnetic flux lines run parallel to the surface near at the equator. However, at the magnetic poles, they dive into the center of the earth. As a result, the compass tries to point both north and down into the ground when you are near the magnetic poles or in the mid latitudes. This results in lead and lag errors.
When you turn through northerly headings, the compass will lag behind the turn. For turns through southerly headings, the compass will lead the turn.
For example, say we are on a west heading and make a right turn to east, while located at 30 degrees north latitude. The compass heading would be accurate when flying west. As the aircraft's heading approaches north, however, the compass heading lags behind the actual heading. When the airplane is really heading north, the compass indicates a 330 heading. As we come around to east, the compass catches up to us and is again accurate.
If that right turn were then continued back to west, the compass would race ahead of our actual heading as we turn. When the actual heading is south, the compass would indicate a 210 heading. As we approach a westerly heading, the lead would dissipate.
So, we see that the compass is accurate when the airplane is flying straight. And, the compass is accurate on east and west headings, even when in a turn. The lead and lag errors are at their worst when turning and when passing through southerly and northerly headings, respectively.
At its worst, the magnitude of the lead and lag error is approximately equal to the latitude at which the airplane is flown. In this example, flown at a 30 degree latitude, the maximum error presented by the compass was 30 degrees.
If you care to understand these errors better, suppose we were flying north and decided to make a right turn to east. We roll into a bank to the right to accomplish this turn. In doing do, we rotate the compass to the right with us. In this situation, the north seeking end of the compass rotates to point down toward the magnetic pole. This causes the compass card to rotate around to display a turn toward the west. After a few seconds the compass begins to follow our right turn to east.
If we performed this same maneuver over the equator, the compass would display no error, because there is no vertical component to the magnetic field.
Acceleration / Deceleration Errors
If the airplane is flown on an east or west heading and it is accelerated, the compass will indicate a turn to the north. If the airplane is slowed, it will indicate a turn to the south. The ANDS acronym is useful for remembering this: Accelerate-North, Decelerate-South.
When flying north or south, no errors will be apparent because of acceleration or deceleration.
Acceleration errors are the result of the design of modern aircraft compass.
If a turn is made from a north heading, the compass will initially indicate a turn in the opposite direction.